# How do you solve -3/(4x) + 3/8 = 27/32?

Mar 24, 2018

$x = - 1.6$

#### Explanation:

$- \frac{3}{4 x} + \frac{3}{8} = \frac{27}{32}$
$- \frac{3}{4 x} = \frac{27}{32} - \frac{3}{8}$
$- \frac{3}{4 x} = \frac{27}{32} - \frac{12}{32}$
$- \frac{3}{4 x} = \frac{15}{32}$
By cross-multiplication:
$4 x \cdot 15 = - 3 \cdot 32$
$60 x = - 96$
$x = - \frac{96}{60}$
$x = - 1.6$

Mar 24, 2018

$x = - \frac{8}{5}$

#### Explanation:

Before we do anything, we need to get a common denominator of $32$.

$- \frac{3}{4} x = - \frac{24}{32} x$ (multiplying top and bottom by 8)

$\frac{3}{8} = \frac{12}{32}$ (multiplying top and bottom by 4)

$\frac{27}{32}$ will stay the same

Thus, we have

$- \frac{24}{32} x + \frac{12}{32} = \frac{27}{32}$

We can subtract $\frac{12}{32}$ from both sides to get

$- \frac{24}{32} x = \frac{15}{32}$

We can cross multiply to get:

$x = \frac{- 24 \cdot \cancel{32}}{\cancel{32} \cdot 15}$

Since the $32$s will cancel, we're left with:

$\frac{- 24}{15}$

Which can be simplified to $x = - \frac{8}{5}$